相关论文: Continuum Model for River Networks

We investigate the dependence of river network scaling on the relative dominance of slope vs. noise in initial conditions, using an erosion model. Increasing slope causes network patterns to transition from dendritic to parallel and results…

Landscapes evolve toward surfaces with complex networks of channels and ridges in response to climatic and tectonic forcing. Here we analyze variational principles giving rise to minimalist models of landscape evolution as a system of…

The universal fractality of river networks is very well known, however understanding of the underlying mechanisms for them is still lacking in terms of stochastic processes. By introducing probability changing dynamically, we have described…

The existence and stability of the universality class associated to local minimal energy landscapes is investigated. Using extensive numerical simulations, we first study the dependence on a parameter $\gamma$ of a partial differential…

A cellular model introduced for the evolution of the fluvial landscape is revisited using extensive numerical and scaling analyses. The basic network shapes and their recurrence especially in the aggregation structure are then addressed.…

River networks serve as a paradigmatic example of all branching networks. Essential to understanding the overall structure of river networks is a knowledge of their detailed architecture. Here we show that sub-branches are distributed…

We consider a model for the formation of a river network in which erosion process plays a role only at the initial stage. Once a global connectivity is achieved, no further evolution takes place. In spite of this, the network reproduces…

The hierarchy of channel networks in landscapes displays features that are characteristic of non-equilibrium complex systems. Here we show that a sequence of increasingly complex ridge and valley networks is produced by a system of partial…

The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method.…

We consider a linearized dynamical system modelling the flow rate of water along the rivers and hillslopes of an arbitrary watershed. The system is perturbed by a random rainfall in the form of a compound Poisson process. The model…

Natural rivers connect to each other to form networks. The geometric structure of a river network can significantly influence spatial dynamics of populations in the system. We consider a process-oriented model to describe population…

This article is the first in a series of three papers investigating the detailed geometry of river networks. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but…

We analyze the Optimal Channel Network model for river networks using both analytical and numerical approaches. This is a lattice model in which a functional describing the dissipated energy is introduced and minimized in order to find the…

A new model to simulate the time evolution of river delta formation process is presented. It is based on the continuity equation for water and sediment flow and a phenomenological sedimentation/ erosion law. Different delta types are…

In this paper, we consider a system of partial differential equations modeling the evolution of a landscape. A ground surface is eroded by the flow of water over it, either by sedimentation or dilution. The system is composed by three…

We study the dynamics of flow-networks in porous media using a pore-network model. First, we consider a class of erosion dynamics assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show…

This study is motivated by problems related to environmental transport on river networks. We establish statistical properties of a flow along a directed branching network and suggest its compact parameterization. The downstream network…

Scaling laws that describe the structure of river networks are shown to follow from three simple assumptions. These assumptions are: (1) river networks are structurally self-similar, (2) single channels are self-affine, and (3) overland…

We analyze the statistics of water droplet avalanches in a continuously driven system. Distributions are obtained for avalanche size, lifetime, and time between successive avalanches, along with power spectra and return maps. For low flow…

Erosion by flowing water is one of the major forces shaping the surface of Earth. Studies in the last decade have shown, in particular, that the drainage region of rivers, where water is collected, exhibits scale invariant features…